The interpretation of this is unclear.
If we assume 16sec(x)cos2(x)-4sec(x)=0,
4sec(x)(4cos2(x)-1)=0, Since sec(x) cannot be zero, 4cos2(x)-1=0,
(2cos(x)-1)(2cos(x)+1)=0, therefore cos(x)=±½, and x=π/3+2πn, 2πn-π/3 (radians) where n is an integer.
In degrees this is x=60+360n, 360n-60.
Another interpretation is 16sec(x)cos2(x)-sec4(x)=0,
sec(x)(16cos2(x)-sec3(x))=0.
Since sec(x) cannot be zero,
16cos2(x)-sec3(x)=0,
16cos5(x)-1=0, 16cos5(x)=1, cos5(x)=1/16, cos(x)=0.5743, x=54.95°+360n, 360n-54.95°. In radians:
x=0.9590+2πn, 2πn-0.9590.